{"id":"06f50703-95a5-47d6-a2cd-2d371639949e","arxiv_id":"2412.05774","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A model-building study showing that a zero lightest neutrino mass can be combined with three right-handed neutrinos and successful low-scale leptogenesis in the scotogenic model.","lead":"This paper builds neutrino mass models in which the lightest neutrino is exactly massless, following a recent cosmological hint. It shows that such models can generate the observed matter-antimatter asymmetry through leptogenesis, especially in the scotogenic framework with TeV-scale right-handed neutrinos.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The PMNS ansatz V=V_CKM^T U_TBM in Eq. (7) is not merely a weak fit but is excluded by the solar angle: its |V_e2|≈0.43 implies sin^2θ12≈0.19, far below the 3σ lower bound of the global fit used in the paper.","rationale":"The reader's weakest-assumption diagnosis is correct and can be sharpened: the problem with Eq. (7) is not merely that 'more than half' of the entries are inside the 3σ range, but that a key phase-independent observable, |V_e2|, is excluded by a large margin. This matters because all of the model's Yukawa alignments are imposed in the TBM basis, so the PMNS matrix is the interface between the algebraic zero-eigenvalue construction and observed neutrino mixing; if that interface fails, the model has no demonstrated connection to data. I nevertheless keep the reader's CONDITIONAL verdict rather than moving to REJECT, for two reasons. First, the algebraic extension to three right-handed neutrinos while preserving a zero eigenvalue is internally consistent and is a legitimate model-building result. Second, the low-scale leptogenesis conclusion in the scotogenic model is substantially independent of the PMNS ansatz: the CP asymmetry in Eq. (26) is basis-invariant under redefinitions of h, and the washout and production estimates are governed by the flavor-texture coefficients rather than by the specific numerical PMNS matrix. But the paper's overall claim to describe 'possible neutrino models' from oscillation data is only conditional on finding a charged-lepton structure that actually fits the data; the Appendix's vector-like lepton extension is a step in that direction but is not worked out to a satisfactory fit either. A quantitative chi-square test of Eq. (7) would decide whether the current ansatz can be used at all or must be replaced before the phenomenological predictions are taken seriously.","tokens_in":16204,"tokens_out":22093,"duration_ms":238485,"concrete_test":"Compute the full chi-square of the predicted PMNS matrix from Eq. (7) against the NuFIT 5.3 global fit, including the 3x3 correlation matrix and the predicted Jarlskog invariant J=4.1e-4. If the resulting p-value is below 1%, the ansatz is excluded at more than 99% CL. As a phase-independent cross-check, compare (sinθ12 cosθ13)^2 implied by |V_e2|=0.43 with the NuFIT 3σ range for sin^2θ12; if the implied value is outside that range, no CP phase can rescue the fit.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central model relies on the PMNS matrix in Eq. (7), built from V=V_CKM^T U_TBM, to connect the zero-eigenvalue construction to neutrino oscillation data. A direct comparison with the NuFIT ranges cited in the paper shows the ansatz is excluded rather than approximate: the predicted |V_e2|≈0.43 corresponds to sin^2θ12≈0.19, well below the 3σ lower bound of the global fit (sin^2θ12≈0.27, giving |V_e2|≈0.52). Because |V_e2|=sinθ12 cosθ13 is independent of the Dirac phase, no choice of CP phases can repair this mismatch. The paper's own acceptance criterion, 'more than half of the V components is included in the 3 sigma range', concedes that several entries are outside; for a unitary 3x3 matrix with strong correlations this is a many-sigma failure, not a mild tension. Since the Yukawa alignment in Eqs. (10) and (17) is imposed in the TBM basis, the only way to reconcile the model with data is through the charged-lepton rotation U_e; taking U_e=V_CKM^T does not accomplish this. Thus the zero-eigenvalue construction is algebraically consistent but has not been shown to be a viable neutrino mass model, and the effective masses in Eqs. (24)-(25) are not genuine predictions of the model unless the charged-lepton sector is modified. The leptogenesis calculation is less affected because epsilon is invariant under unitary redefinitions of h, as noted in footnote e, but the paper's stated motivation of studying models 'from a viewpoint of neutrino oscillation data' is undercut by the failed mixing ansatz.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies seesaw and scotogenic neutrino-mass models with a vanishing light neutrino mass eigenvalue, extending the usual two-right-handed-neutrino construction to three right-handed neutrinos while keeping the zero eigenvalue. The neutrino-sector mixing is taken tribimaximal, and the charged-lepton rotation is assumed to be the CKM matrix, giving the PMNS ansatz in Eq. (7). From the zero-mass assumption and the measured squared-mass differences the authors derive the absolute masses m2 = 0.0087 eV and m3 = 0.0503 eV for normal ordering, compute the effective masses for neutrinoless double beta decay and beta decay, and analyze thermal leptogenesis. The main phenomenological result is that successful leptogenesis can occur in the scotogenic model for MN1 as low as about 10^4 GeV, in contrast to the type-I seesaw lower bound around 3 x 10^9 GeV.","tokens_in":16805,"tokens_out":9035,"duration_ms":94388,"significance":"The algebraic construction is transparent, and the leptogenesis analysis has a genuinely useful feature: the CP asymmetry in Eq. (26) is invariant under unitary redefinitions of the neutrino Yukawa couplings, so that part of the paper is not entangled with the PMNS fit. If the mixing ansatz Eq. (7) were compatible with data, the paper would offer a concrete zero-eigenvalue framework with definite predictions for m_beta_beta, m_beta, and the sum of neutrino masses, as well as an interesting new production mechanism for the lightest right-handed neutrino through scattering mediated by the singlet scalar S. However, the assumed PMNS matrix is not a mild approximation but is excluded by the measured solar angle, and the exclusion of the inverted ordering rests on an unsupported reading of the neutrinoless double beta decay bound. These are load-bearing problems for the paper's phenomenological claims. The paper is also clearly written and the derivations are mostly easy to follow, but the central data-compatibility claim fails.","major_comments":[{"comment":"The PMNS ansatz V = V_CKM^T U_TBM is not merely in mild tension with neutrino oscillation data; it is excluded by the solar angle. Using the absolute values in Eq. (7), sin^2(theta_12) = |V_e2|^2 / (1 - |V_e3|^2) ≈ 0.43^2 / 0.978 ≈ 0.19, far below the 3-sigma lower bound of about 0.27 in the global fit cited in the paper. Since theta_12 is independent of the Dirac CP phase, no choice of phases can repair this mismatch, and the appendix's vector-like lepton extension, Eq. (37), still has |V_e2| = 0.43. The statement that 'more than half of the V components is included in the 3 sigma range' is not an adequate acceptance criterion for a unitary matrix, because individual elements are correlated; the mismatch in |V_e2| alone corresponds to a many-sigma failure. All subsequent phenomenological outputs, including the effective masses in Eqs. (24)-(25), depend on the assumed charged-lepton sector, so the model as presented has not been shown to reproduce the measured neutrino mixing matrix.","section":"§2, Eq. (7)"},{"comment":"The inverted ordering is dismissed because 'the present bound for the neutrinoless double beta decay may have excluded the model already.' Equation (24) gives m_beta_beta = 0.049 eV for IO, whereas the KamLAND-Zen bound quoted in the paper is in the range 36-156 meV, or 28-122 meV depending on the nuclear matrix elements. The IO prediction is therefore not excluded by this bound. The authors may wish to argue that IO is disfavored by cosmological data, but the paper itself stresses that the cosmological bound is model-dependent and that it is premature to base strong conclusions on it. The unsupported exclusion of IO should be removed or replaced by a quantitative discussion of the actual constraint.","section":"§2, after Eq. (24), and §4"},{"comment":"The numerical leptogenesis analysis uses |epsilon| ~ 10^-7 and the estimate Y_L = epsilon Y_N1^eq as if these conditions guarantee the observed baryon asymmetry, but the final asymmetry depends on the full Boltzmann dynamics, including the delay of the N1 decay controlled by h1. The rate estimates and Fig. 4 support this for the chosen benchmark, but the region of parameter space in which the no-washout estimate is quantitatively accurate is not mapped. This should be presented as an order-of-magnitude estimate rather than as a derivation, or supplemented by a scan over h1 and the right-handed neutrino mass ratios.","section":"§3.1, Eq. (26) and text after Eq. (29)"}],"minor_comments":[{"comment":"There are numerous typos and malformed references, including 'on the oher hand', 'scotgenic', 'chrged', 'exteriment', 'Collabolation', 'α=e,µ.τ' in Eq. (1), and 'arXiv:2407.18047 [astro-phCO]' in Ref. [7]. These should be corrected in a revised version.","section":"Throughout"},{"comment":"The washout cross section in Eq. (34) contains terms involving M_eta, but it is then applied to both the scotogenic model and the type-I seesaw model in Fig. 3. For the type-I case the limit M_eta -> infinity, or a separate formula, should be given explicitly.","section":"§3.3, Eq. (34)"},{"comment":"The parameter n is used in the exponents before its definition through MN3 = 10^n MN1 is recalled in Fig. 1; defining n once near Eq. (29) would make the bounds on h1 much easier to parse.","section":"§3.1, Eqs. (29)-(31)"},{"comment":"The notation in Eq. (35), in particular the inequality F F^dagger > M_E^2, is dimensionally ambiguous because F is a coupling while M_E is a mass. Please specify the mass dimension of F and state the condition in dimensionless form.","section":"Appendix, Eq. (35)"},{"comment":"The statement in the introduction that the three-right-handed-neutrino extension 'is found to be supported by imposing that the baryon number asymmetry is generated through thermal leptogenesis' is stronger than what is shown: the two-right-handed-neutrino model gives epsilon = 0 only for the specific TBM-aligned flavor structure used here, as footnote f itself acknowledges. The claim should be made conditional on that flavor structure.","section":"§3.1, footnote f and Introduction"}],"recommendation":"reject","confidential_remarks":"For the editor: the decisive issue is the quantitative failure of the PMNS ansatz in Eq. (7). I confirmed independently that it gives sin^2(theta_12) ≈ 0.19, below the 3-sigma range of the global fit cited by the authors. This is not a matter of taste or a mild tension, and the appendix does not repair it. The unsupported exclusion of the IO case is a separate correctable issue. I see no sign of misconduct; the recommendation is based solely on the load-bearing technical problems."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First: there is a real idea here. Keeping a zero neutrino mass eigenvalue while adding a third right-handed neutrino is a neat trick, and the paper works out the Yukawa conditions cleanly. The extension is motivated by leptogenesis, and the CP asymmetry calculation is standard and internally consistent. The genuinely new bit is the S-mediated scattering that can bring N1 into thermal equilibrium in the scotogenic model even when h1 is tiny, which opens a plausible low-scale leptogenesis window around 10^4 GeV. The washout analysis is careful, and the Boltzmann evolution in Fig. 4 is a nice check. That part deserves credit.\n\nThe problem is the PMNS matrix. The ansatz V = V_CKM^T U_TBM gives |V_e2| ≈ 0.43, which implies sin^2 θ12 ≈ 0.19. That is below the 3σ lower bound of the NuFIT analysis the paper itself cites. Since |V_e2| = sin θ12 cos θ13, no CP phase can change this. The paper's own acceptance criterion—'more than half of the V components is included in the 3σ range'—understates the issue: for a unitary matrix with correlated entries, one element sitting many sigma outside the allowed range is a fatal tension, not a mild one. The appendix's vector-like lepton modification changes the Jarlskog invariant but leaves |V_e2| unchanged, so it does not rescue the solar angle. Consequently, the effective masses in eqs. (24)–(25) are not genuine predictions of the model as presented. The absolute mass scale itself is also conditional: m2 and m3 are fixed from the observed mass splittings plus the zero-eigenvalue input, so the sum 0.059 eV is a restatement of the assumption, not an independent prediction.\n\nThe IO treatment is another soft spot. The paper says the KamLAND-Zen bound 'may have excluded' the IO and then drops it; that deserves a sharper argument. The leptogenesis part is less affected because ε is invariant under unitary redefinitions of h, as the paper notes, so the low-scale leptogenesis result can survive even if the mixing ansatz is replaced.\n\nOverall: the model-building core is sound and worth a referee's time, but the phenomenological connection to oscillation data is currently broken. The audience is neutrino model-builders, especially those working on scotogenic leptogenesis; they will find the mechanism worth examining. I would send it to peer review, with the expectation that the charged-lepton sector must be fixed or the phenomenological claims explicitly conditional.","headline":"A clever zero-mass construction and a careful leptogenesis analysis, undermined by a PMNS ansatz the solar angle already rules out.","tokens_in":17219,"tokens_out":3517,"would_cite":false,"duration_ms":35805,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A zero neutrino mass eigenvalue survives adding a third right-handed neutrino, and the extension makes thermal leptogenesis viable at the TeV scale in the scotogenic model.","keywords":["neutrino mass","zero mass eigenvalue","seesaw mechanism","scotogenic model","tribimaximal mixing","leptogenesis","normal mass ordering","neutrinoless double beta decay"],"falsifier":"A decisive observation would be a precise measurement of the lightest neutrino mass: with normal ordering the model requires $m_1 = 0$ and $\\sum_j m_j = 0.059$ eV, so any reliable determination with $m_1 > 0$ (or a mass sum clearly above $0.07$ eV while normal ordering is favored) would falsify this branch. For the inverted-ordering version, the model predicts $m_{\\beta\\beta} = 0.049$ eV, so next-generation neutrinoless double $\\beta$ decay searches that push the limit below roughly $0.01$ eV with no signal would exclude it.","tokens_in":16016,"feed_emoji":"⚛️","tokens_out":11541,"duration_ms":95055,"temperature":0.7,"pith_summary":"The paper argues that cosmological hints favoring a zero lightest neutrino mass can be realized in seesaw-type models with three right-handed neutrinos, not just the minimal two. It starts from the known fact that two right-handed neutrinos produce one zero mass eigenvalue, then adds a third neutrino while keeping that eigenvalue zero through special Yukawa flavor patterns. The extension is not cosmetic: it is needed for thermal leptogenesis, because with only two right-handed neutrinos the CP asymmetry vanishes under the assumed flavor structure. With normal mass ordering, the model fixes the absolute masses at $m_2 = 0.0087$ eV and $m_3 = 0.0503$ eV, giving $\\sum_j m_j = 0.059$ eV, and predicts effective masses of $m_{\\beta\\beta} = 0.0035$ eV for neutrinoless double $\\beta$ decay and $m_\\beta = 0.0086$ eV for $\\beta$ decay; the inverted-ordering version predicts $m_{\\beta\\beta} = 0.049$ eV and may already conflict with the current bound. In the scotogenic version, the same construction allows successful leptogenesis with the lightest right-handed neutrino as light as about $10^4$ GeV, far below the usual $3\\times10^9$ GeV seesaw bound.","feed_headline":"Zero neutrino mass eigenvalue makes TeV-scale leptogenesis work","feed_subtitle":"A third right-handed neutrino keeps the zero mass and generates baryon asymmetry at 10^4 GeV in the scotogenic model.","key_machinery":"The central object is the seesaw-type neutrino mass matrix $(M_\\nu)_{\\alpha\\beta} = \\sum_k h^\\nu_{\\alpha k} h^\\nu_{\\beta k} e^{i\\gamma}\\Lambda_k$, where $\\Lambda_k = \\langle\\phi\\rangle^2/M_{N_k}$ in the type-I seesaw model and is the one-loop expression in eq. (5) in the scotogenic model (a radiative neutrino mass model with an inert doublet and a dark matter candidate). A tribimaximal mixing matrix $U_\\nu$ diagonalizes $M_\\nu$, and the PMNS matrix is constructed as $V = V_{\\rm CKM}^T U_{\\rm TBM}$, motivated by the SU(5) relation $M_e = M_d^T$ between charged-lepton and down-quark mass matrices. The special Yukawa flavor patterns (10) and (17) keep one eigenvalue zero after the third right-handed neutrino is added, while the complex relative phase in the extended mass term provides CP violation. The decay-asymmetry formula (26), with its flavor-structure coefficients, carries the leptogenesis calculation.","core_discovery":"The central claim is that a model built on the PMNS ansatz $V = V_{\\rm CKM}^T U_{\\rm TBM}$ -- tribimaximal mixing in the neutrino sector combined with charged-lepton mixing inherited from the CKM matrix -- can support a zero neutrino mass eigenvalue even after three right-handed neutrinos are introduced. The Yukawa couplings must obey the flavor relations in eqs. (10) and (17), and the third right-handed neutrino receives its mass from $M_j + \\Delta M$ with $\\Delta M = M_0 e^{i\\xi}$, whose phase relative to the singlet VEV generates the CP asymmetry in $N_1$ decay. This extension is argued to be necessary for leptogenesis to work in this setup. Using neutrino oscillation data, the normal-ordering absolute masses come out as $m_2 = 0.0087$ eV and $m_3 = 0.0503$ eV; the inverted-ordering version predicts $m_{\\beta\\beta} = 0.049$ eV, close enough to the current neutrinoless double $\\beta$ decay bound that the paper treats the normal ordering as the viable branch.","pith_inferences":["If the same zero-eigenvalue construction is carried over to other radiative mass models, the low-scale leptogenesis mechanism should survive as long as $\\Lambda_k$ can be small at TeV-scale $N_k$ masses; the scotogenic model is the paper's concrete example rather than the only possible host.","The ansatz $V = V_{\\rm CKM}^T U_{\\rm TBM}$ directly ties quark mixing to lepton mixing, so a precise determination of the Dirac CP phase that is incompatible with the predicted Jarlskog invariant $J \\simeq 4\\times10^{-4}$ (or the appendix's $J = -0.009$) would cast doubt on the whole construction.","The small allowed range of $h_1$ implies a long-lived lightest right-handed neutrino, so searches for displaced or late decays of TeV-scale neutral fermions could probe this scenario even if direct pair production is beyond reach.","The late $N_1$ decay also makes $N_1$ a natural common source for the baryon asymmetry and for the dark matter abundance, giving the scotogenic branch a phenomenological link that the type-I seesaw branch lacks."],"forward_implications":["In the normal ordering, the zero lightest mass fixes the mass sum at $\\sum_j m_j = 0.059$ eV, giving future cosmological probes of the neutrino mass sum a narrow target to confirm or exclude.","The inverted-ordering version predicts $m_{\\beta\\beta} = 0.049$ eV, so continued improvement of neutrinoless double beta decay bounds without a signal would eliminate that branch.","In the scotogenic model, $N_1$ can be as light as about $10^4$ GeV and still generate the observed baryon asymmetry, placing the right-handed neutrinos closer to accelerator reach than in high-scale seesaw.","The singlet-scalar scattering $N_k N_k \\to N_1 N_1$ can thermally produce the lightest right-handed neutrino even when its Yukawa coupling $h_1$ is very small, and the small $h_1$ delays $N_1$ decay until washout has frozen out.","In the normal-ordering branch, the predicted effective masses $m_{\\beta\\beta} = 0.0035$ eV and $m_\\beta = 0.0086$ eV are below current experimental sensitivity, so this version of the model would show up first in mass-sum cosmology rather than in decay searches."],"supporting_citations":[{"why":"Supplies the seesaw mechanism that generates the Majorana neutrino mass matrix used throughout.","marker":"[8]"},{"why":"Introduces the scotogenic model, whose loop-suppressed $\\Lambda_k$ permits TeV-scale right-handed neutrino masses.","marker":"[9]"},{"why":"Supplies the tribimaximal mixing matrix $U_\\nu$ that underlies the zero-eigenvalue construction.","marker":"[13]"},{"why":"Defines the CKM matrix used in the PMNS ansatz $V = V_{\\rm CKM}^T U_{\\rm TBM}$.","marker":"[16]"},{"why":"Gives the SU(5) mass relation $M_e = M_d^T$ that motivates taking the charged-lepton mixing to be essentially the CKM matrix.","marker":"[17]"},{"why":"Provides the neutrino oscillation data that fix $m_2$ and $m_3$ in eq. (18).","marker":"[1]"},{"why":"Provides the 3-neutrino global fit against which the constructed PMNS matrix is checked.","marker":"[18]"},{"why":"Establishes leptogenesis as the mechanism that converts $N_1$ decay into the baryon asymmetry.","marker":"[25]"},{"why":"Supplies the standard formula for the CP asymmetry $\\varepsilon$ in $N_1$ decay used in eq. (26).","marker":"[26]"},{"why":"Gives the usual lower bound on $M_{N_1}$ for type-I leptogenesis that the scotogenic branch avoids.","marker":"[27]"}],"fun_headline_variants":["Zero neutrino mass enables TeV leptogenesis","TeV leptogenesis from zero neutrino mass","Zero mass eigenvalue unlocks TeV-scale leptogenesis","Zero-mass neutrino model predicts normal ordering","TeV-scale leptogenesis with zero neutrino mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the charged-lepton diagonalization matrix is essentially the CKM matrix, so the PMNS matrix equals $V = V_{\\rm CKM}^T U_{\\rm TBM}$; the paper itself notes that only more than half of the elements of this $V$ lie inside the 3$\\sigma$ range of the global fit, so if the real charged-lepton mixing differs, the predicted mixing angles, the zero eigenvalue, and the fixed mass values lose their anchor.","fun_headline_variants_meta":{"raw":{"variants":["Zero neutrino mass enables TeV leptogenesis","TeV leptogenesis from zero neutrino mass","Zero mass eigenvalue unlocks TeV-scale leptogenesis","Zero-mass neutrino model predicts normal ordering","TeV-scale leptogenesis with zero neutrino mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000488,"raw_usage":{"total_tokens":2368,"prompt_tokens":871,"completion_tokens":1497,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":487,"completion_tokens_details":{"reasoning_tokens":1430}},"tokens_in":487,"tokens_out":1497,"duration_ms":11642,"temperature":1.0,"reasoning_tokens":1430,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:23:00.473854+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive observation would be a precise measurement of the lightest neutrino mass: with normal ordering the model requires $m_1 = 0$ and $\\sum_j m_j = 0.059$ eV, so any reliable determination with $m_1 > 0$ (or a mass sum clearly above $0.07$ eV while normal ordering is favored) would falsify this branch. For the inverted-ordering version, the model predicts $m_{\\beta\\beta} = 0.049$ eV, so next-generation neutrinoless double $\\beta$ decay searches that push the limit below roughly $0.01$ eV with no signal would exclude it.","supporting_citations":[{"cited_title":"Minkowski, Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the seesaw mechanism that generates the Majorana neutrino mass matrix used throughout."},{"cited_title":"Ma, Phys","cited_arxiv_id":null,"evidence_quote":"Introduces the scotogenic model, whose loop-suppressed $\\Lambda_k$ permits TeV-scale right-handed neutrino masses."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the tribimaximal mixing matrix $U_\\nu$ that underlies the zero-eigenvalue construction."},{"cited_title":"Suematsu, Phys","cited_arxiv_id":null,"evidence_quote":"Gives the SU(5) mass relation $M_e = M_d^T$ that motivates taking the charged-lepton mixing to be essentially the CKM matrix."},{"cited_title":"Estentau et al., JHEP 12 (2024) 216","cited_arxiv_id":null,"evidence_quote":"Provides the 3-neutrino global fit against which the constructed PMNS matrix is checked."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the standard formula for the CP asymmetry $\\varepsilon$ in $N_1$ decay used in eq. (26)."},{"cited_title":"Davidson and A","cited_arxiv_id":null,"evidence_quote":"Gives the usual lower bound on $M_{N_1}$ for type-I leptogenesis that the scotogenic branch avoids."}],"review_version":1}